The following databases will lead you to articles in journals in the fields of anthropology and sociology.
SocINDEX with Full Text contains full text for over 400 journals in Sociology with some text dating back to 1895. This database also includes full text for more than 700 books and monographs, and full text for 6,800 conference papers.
AnthroSource provides the full text of over 30 journals published by the American Anthropological Association. See the search tips.
Academic Search Complete indexes over 9,300 periodicals in many disciplines, providing over 5,300 journals in full text.
JSTOR includes access to full-text archives of several titles in the fields of anthropology and sociology.
Project MUSE provides the full text of a several journals in sociology and a handful in anthropology.